-(x+6)(x+4)=x(x+11+6)-

Solution for -(x+6)(x+4)=x(x+11+6)- equation:

-(x+6)(x+4)=x(x+11+6)-

We move all terms to the left:

-(x+6)(x+4)-(x(x+11+6)-)=0

We add all the numbers together, and all the variables

-(x+6)(x+4)-(x(x+17)-)=0

We multiply parentheses ..

-(+x^2+4x+6x+24)-(x(x+17)-)=0


We calculate terms in parentheses: -(x(x+17)-), so:

x(x+17)-

We add all the numbers together, and all the variables

x(x+17)

We multiply parentheses

x^2+17x

Back to the equation:

-(x^2+17x)


We get rid of parentheses

-x^2-x^2-4x-6x-17x-24=0

We add all the numbers together, and all the variables

-2x^2-27x-24=0

a = -2; b = -27; c = -24;
Δ = b2-4ac
Δ = -272-4·(-2)·(-24)
Δ = 537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{537}}{2*-2}=\frac{27-\sqrt{537}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{537}}{2*-2}=\frac{27+\sqrt{537}}{-4}
$